I saw this translated in the first episode of FLCL as "It's wrong.", but checking the translation, I get "Different." Could someone clear this up?
ちがいます the speaker intends to convey:
"The situation/case/concept that I think you are thinking of is different from the situation/case/concept I believe I am currently experiencing".
This underlying meaning can be translated to a variety of English expressions not limited to "no" or "you're/(s)he's/it's/that's wrong".
Based on the anime that I've seen, when a character uses ちがいます in essence what they are saying (in a nutshell) is:
No, what you said is different from what I said/thought/felt, therefore it is wrong/not correct.
Normally, this is just expressed/translated as: You're wrong, He's wrong, She's wrong, or It's wrong. Depending on the context.
This is interesting. 違う was originally written as 違ふ. And, in 10th century, the meaning was slightly different. The original meaning was
互いに交差したり行き違ったりする (Two things intersect with each other. Two people try to go to each other's place and fail to meet.) http://kobun.weblio.jp/content/%E3%81%A1%E3%81%8C%E3%81%B5
There were several derived meanings such as "fail to meet. avoid to meet. go to a wrong direction. make something different. change something. disobey. being different."
According to this dictionary, デジタル大辞泉 https://kotobank.jp/word/%E9%81%95%E3%81%86-559103 ,
the first meaning is still used in compound verbs such as
行き違う (Two people try to go to each other's place and fail to meet.)
すれ違う (pass each other.)
But, they are now the fifth meaning on 大辞林.
Other meanings are follows.
1 . a "being different"
- 習慣が違う。 (The customs are different.)
1 . b "There is a gap. being better comparing to others."
- 格が違う。 (being in a better class.)
2 . "What someone expected or thought is different from the current situation."
- 話が違う。 (The things you told me were different from the current situation.)
- 約束と違う。 (The promise is not kept.)
3 . "being wrong."
- 計算が違う。 (The calculation is wrong.)
4 . "Not in the right position."
- 筋が違う。 (getting a crick. (The muscle is not in the right position.))
- 気が違う。 (being mad. (The mind is not in the right position.))
It seems that their basic idea is "fail to meet."
Back to the original question, it means no. And,「いいえ、違います。」 is one of the most appropriate way (in elementary school) to answer no.
I think 違う (違います ちゃう ちげー) are used more than いいえ to say no.